Phi Theory

This book brings together the different strands and styles of research on Phi-features, such as person, number, and gender. It presents the core questions, major results, and new directions of this area of linguistic theory and shows how Phi Theory casts light on the nature of interfaces and the structure of the grammar.

This title is printed in full color throughout. From one of the most original and influential neuroscientists at work today, here is an exploration of consciousness unlike any other—as told by Galileo, who opened the way for the objectivity of science and is now intent on making subjective experience a part of science as well. Galileo’s journey has three parts, each with a different guide. In the first, accompanied by a scientist who resembles Francis Crick, he learns why certain parts of the brain are important and not others, and why consciousness fades with sleep. In the second part, when his companion seems to be named Alturi (Galileo is hard of hearing; his companion’s name is actually Alan Turing), he sees how the facts assembled in the first part can be unified and understood through a scientific theory—a theory that links consciousness to the notion of integrated information (also known as phi). In the third part, accompanied by a bearded man who can only be Charles Darwin, he meditates on how consciousness is an evolving, developing, ever-deepening awareness of ourselves in history and culture—that it is everything we have and everything we are. Not since Gödel, Escher, Bach has there been a book that interweaves science, art, and the imagination with such originality. This beautiful and arresting narrative will transform the way we think of ourselves and the world.

In recent years, developments in experimental philosophy have led many thinkers to reconsider their central assumptions and methods. It is not enough to speculate and introspect from the armchair—philosophers must subject their claims to scientific scrutiny, looking at evidence and in some cases conducting new empirical research. The Theory and Practice of Experimental Philosophy is an introduction and guide to the systematic collection and analysis of empirical data in academic philosophy. This book serves two purposes: first, it examines the theory behind “x-phi,” including its underlying motivations and the objections that have been leveled against it. Second, the book offers a practical guide for those interested in doing experimental philosophy, detailing how to design, implement, and analyze empirical studies. Thus, the book explains the reasoning behind x-phi and provides tools to help readers become experimental philosophers.

A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University

This monograph investigates the modular architecture of language through the nature of "uninterpretable" phi-features: person, number, gender, and Case. It provides new tools and evidence for the modular architecture of the human language faculty, a foundational topic of linguistic research. At the same time it develops a new theory for one of the core issues posed by the Minimalist Program: the relationship of syntax to its interfaces and the nature of uninterpretable features. The work sets out to establish a new cross-linguistic phenomenon to study the foregoing, person-governed last-resort repairs, which provides new insights into the nature of ergative/accusative Case and of Case licensing itself. This is the first monograph that explicitly addresses the syntactic vs. morphological status of uninterpretable phi-features and their relationship to interface systems in a similar way, drawing on person-based interactions among arguments as key data-base.

Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.

This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition.Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages. The diagrams correspond to integrals in momentum space. They are evaluated in 4-î dimensions, where they possess pole terms in 1/î. The pole terms are collected into renormalization constants.The theory of the renormalization group is used to find the critical scaling laws. They contain critical exponents which are obtained from the renormalization constants in the form of power series. These are divergent, due to factorially growing expansion coefficients. The evaluation requires resummation procedures, which are performed in two ways: (1) using traditional methods based on Pad‚ and Borel transformations, combined with analytic mappings; (2) using modern variational perturbation theory, where the results follow from a simple strong-coupling formula. As a crucial test of the accuracy of the methods, the critical exponent à governing the divergence of the specific heat of superfluid helium is shown to agree very well with the extremely precise experimental number found in the space shuttle orbiting the earth (whose data are displayed on the cover of the book).The phi4-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of phi4-theories are sketched, such as variational perturbation expansions in three rather than 4-î dimensions, and improved ratio tests in high-temperature expansions of lattice models.

A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.